Thompson, 67, lost his fight against prostate cancer in the early hours.
United said they were 'devastated' by the death of one of their most loyal backers who was 'a very close and inspirational friend'.
Thompson won much admiration in the football world and was seen as a champion of the smaller clubs in the Scottish Premier League.
Despite his debilitating illness over the past few years, he continued with his duties at Tannadice as long as he could.
He also insisted on supporting his team in person as much as possible, both home and away.
The club said in a statement on their website, www.dundeeunitedfc.co.uk: 'It is with great sadness that Dundee United announce the death of chairman Eddie Thompson, who died today after a long illness borne with great fortitude, much bravery and a dogged determination to carry out his responsibilities at Tannadice for as long as possible.'
The news comes only three days after the death of his son-in-law Ken Mitchell, 38, who died in a motorcycle accident.
Thompson had been battling cancer over the past few years and received specialist treatment at Ninewells Hospital, Dundee.
But despite these efforts, the disease could not be prevented from spreading.
He is survived by his wife Cath, children Justine and Stephen and four grandchildren.
Born in Glasgow in 1940, he moved to Dundee in 1964 and began to support the club.
He was a trained accountant and successful businessman and was keen to bring these business links to bear at Dundee United.
Thompson became chairman and owner in September 2002 after acquiring a majority shareholding.
Since that day, he has ploughed millions of pounds of his own money into Dundee United.
In June 2007, the club was mired in record levels of debt, which stood at £2.7million. By June 2008, this had turned into an operating profit.
But despite his financial backing and business-like approach to handling the side, he saw himself above all as a supporter and believed Dundee United fans were the club's true owners.
He was once quoted as saying: 'You can change your wife, your house, your car, but you can never change your team.
'Chairmen come and go, boards come and go, but the fans remain. They are the one true constant.'
One of the stands at Tannadice was named after him earlier this year and thousands of Dundee United fans wore "One Eddie Thompson" T-shirts at this year's CIS Cup final.
Motherwell chairman John Boyle paid tribute to Thompson as a champion of the smaller clubs in Scotland's top flight.
'He fought for his club, he was so enthusiastic and so passionate,' Boyle told BBC Radio Scotland.
'He was an inspiration to us.
'There was absolutely no question that, as he said, he was the custodian for the fans.
'Dundee United went through a very, very turbulent time and he was a bit of stability for the club.
'They have achieved marvels in the last six or seven years, largely due to his influence. The players, the manager and the fans all looked up to him so much.
'He has left the club in a tremendously good nick.
'He fought for all of the smaller clubs. He was a director of the SPL for many years and everyone will tell you, they may have disagreed with him, but there was enormous respect for him."'
Mike Barile, associate director of the Dundee United supporters' group Arab Trust and a close friend of Thompson, described him as 'just a lovely, lovely man'.
Barile said: 'Eddie was so passionate about his football team, and through his hard work and determination he proved his doubters wrong and turned things around here.
'He was a real workaholic and that explains a lot of his success in business - once he decided what he wanted to do that is what he did.
'But at the same time he also allocated time to his wife and family, and I can remember my wife once remarking about what a gentleman he was with Cath.
'Whether Eddie was speaking to a taxi driver or whoever, he gave that individual his full attention and was genuinely interested in them - that was a remarkable gift.'
